JEE Advanced · 2010 · 11 Apr 2010 · Paper 1 · Rotational Mechanics

A binary star consists of two stars A (mass

2.2 M_{s}

) and B (mass

11 M_{s}

), where

M_{s}

is the mass of the sun. They are separated by distance

d

and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is

Answer: 6

Solution

Let

r_{1}

and

r_{2}

be the distances of stars A and B from the centre of mass, respectively.

Since the centre of mass is stationary:

m_{1} r_{1} = m_{2} r_{2}

2.2 M_{s} \cdot r_{1} = 11 M_{s} \cdot r_{2}

r_{1} = 5 r_{2}

Also,

r_{1} + r_{2} = d

, so

r_{2} = d /6

and

r_{1} = 5 d /6

.

Both stars have the same angular velocity

ω

. The angular momentum of star A about the centre of mass is:

L_{A} = m_{1} r_{1}^{2} ω = 2.2 M_{s} \cdot (5 r_{2})^{2} ω = 55 M_{s} r_{2}^{2} ω

The angular momentum of star B about the centre of mass is:

L_{B} = m_{2} r_{2}^{2} ω = 11 M_{s} r_{2}^{2} ω

Total angular momentum:

L_{total} = L_{A} + L_{B} = 55 M_{s} r_{2}^{2} ω + 11 M_{s} r_{2}^{2} ω = 66 M_{s} r_{2}^{2} ω

The ratio:

\frac{L _{total}}{L _{B}} = \frac{66 M _{s} r _{2}^{2} ω}{11 M _{s} r _{2}^{2} ω} = 6

JEE Advanced · 2010 · 11 Apr 2010 · Paper 1 · Integer answer

Practise more: all JEE Advanced PYQs on Rotational Mechanics →

JEE Advanced · 2010 · 11 Apr 2010 · Paper 1 · Rotational Mechanics

Solution

More JEE Advanced questions on Rotational Mechanics